This paper introduces a novel generative modeling framework grounded in phase space dynamics, taking inspiration from the principles underlying Critically Damped Langevin Dynamics (CLD). Leveraging insights from stochastic optimal control, we construct a favorable path measure in the phase space that proves highly advantageous for generative sampling. A distinctive feature of our approach is the early-stage data prediction capability within the context of propagating generating Ordinary Differential Equations (ODEs) or Stochastic Differential Equations (SDEs) processes. This early prediction…
A central issue in machine learning is how to train models on sensitive user data. Industry has widely adopted a simple algorithm: Stochastic Gradient Descent with noise (a.k.a. Stochastic Gradient Langevin Dynamics). However, foundational theoretical questions about this algorithm's privacy loss remain open -- even in the seemingly simple setting…
Normalizing flows (NFs) are end-to-end likelihood-based generative models for continuous data, and have recently regained attention with encouraging progress on image generation. Yet in the video generation domain, where spatiotemporal complexity and computational cost are substantially higher, state-of-the-art systems almost exclusively rely on diffusion-based models. In this work, we revisit…
Discrete diffusion models have emerged as strong alternatives to autoregressive language models, with recent work initializing and finetuning a base unimodal model for bi-modal generation. Diverging from previous approaches, we introduce the first tri-modal Masked Diffusion Models (MDM) pretrained from scratch on text, image-text, and audio-text data. We systematically analyze…